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A Correlated Queue

Published online by Cambridge University Press:  14 July 2016

B.W. Conolly  and
N. Hadidi
N. Hadidi
Affiliation:
Virginia Polytechnic Institute
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Abstract

A “correlated queue” is defined to be a queueing model in which the arrival pattern influences the service pattern or vice versa. A particular model of this nature is considered in this paper. It is such that the service time of a customer is directly proportional to the interval between his own arrival and that of his predecessor. The initial busy period, state and output processes are analyzed in detail. For completeness, a sketch is also given of the analysis of the waiting time process which forms the subject of another paper. The results are used in the analysis of the state and output processes.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 1 , April 1969 , pp. 122 - 136
Copyright
Copyright © Applied Probability Trust 

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References

Conolly, B. W. (1968) The waiting time process for a certain correlated queue. Operat. Res. 16, 1006–1015.CrossRefGoogle Scholar
Cox, D. R. and Smith, W. L. (1961) Queues. Methuen & Co. Ltd., London.Google Scholar
Harris, C. H. (1967) Queues with state dependent stochastic service rates. Operat. Res. 15, 117–130.CrossRefGoogle Scholar
John, F. I. (1963) Single server queue with dependent service and interarrival intervals. J. Soc. Indust. Appl. Math. 11, 526–534.CrossRefGoogle Scholar
Lindley, D. V. (1952) The theory of queues with a single server. Proc. Camb. Phil. Soc. 48, 277–289.CrossRefGoogle Scholar
Prabhu, N. U. (1960) Some results for a queue with Poisson arrivals. J. R. Statist. Soc. B 22, 104–107.Google Scholar
Prabhu, N. U. (1965) Queues and Inventories. Wiley Inc., New York, 81–85.Google Scholar